details

property	value
status	complete
benchmark	#3.55.xml
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n140.star.cs.uiowa.edu
space	AG01

run statistics

property	value
solver	AProVE
configuration	rcdcRelativeAlsoLower
runtime (wallclock)	298.917 seconds
cpu usage	1168.07
user time	1156.93
system time	11.1367
max virtual memory	1.9248832E7
max residence set size	1.4769664E7

stage attributes

key	value
starexec-result	WORST_CASE(Omega(n^1), ?)

output

WORST_CASE(Omega(n^1), ?) proof of /export/starexec/sandbox/benchmark/theBenchmark.xml # AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty The Derivational Complexity (innermost) of the given DCpxTrs could be proven to be BOUNDS(n^1, INF). (0) DCpxTrs (1) DerivationalComplexityToRuntimeComplexityProof [BOTH BOUNDS(ID, ID), 0 ms] (2) CpxRelTRS (3) SInnermostTerminationProof [BOTH CONCRETE BOUNDS(ID, ID), 389 ms] (4) CpxRelTRS (5) RelTrsToDecreasingLoopProblemProof [LOWER BOUND(ID), 0 ms] (6) TRS for Loop Detection (7) DecreasingLoopProof [LOWER BOUND(ID), 0 ms] (8) BEST (9) proven lower bound (10) LowerBoundPropagationProof [FINISHED, 0 ms] (11) BOUNDS(n^1, INF) (12) TRS for Loop Detection ---------------------------------------- (0) Obligation: The Derivational Complexity (innermost) of the given DCpxTrs could be proven to be BOUNDS(n^1, INF). The TRS R consists of the following rules: minus(x, 0) -> x minus(s(x), s(y)) -> minus(x, y) quot(0, s(y)) -> 0 quot(s(x), s(y)) -> s(quot(minus(x, y), s(y))) le(0, y) -> true le(s(x), 0) -> false le(s(x), s(y)) -> le(x, y) app(nil, y) -> y app(add(n, x), y) -> add(n, app(x, y)) low(n, nil) -> nil low(n, add(m, x)) -> if_low(le(m, n), n, add(m, x)) if_low(true, n, add(m, x)) -> add(m, low(n, x)) if_low(false, n, add(m, x)) -> low(n, x) high(n, nil) -> nil high(n, add(m, x)) -> if_high(le(m, n), n, add(m, x)) if_high(true, n, add(m, x)) -> high(n, x) if_high(false, n, add(m, x)) -> add(m, high(n, x)) quicksort(nil) -> nil quicksort(add(n, x)) -> app(quicksort(low(n, x)), add(n, quicksort(high(n, x)))) S is empty. Rewrite Strategy: INNERMOST ---------------------------------------- (1) DerivationalComplexityToRuntimeComplexityProof (BOTH BOUNDS(ID, ID)) The following rules have been added to S to convert the given derivational complexity problem to a runtime complexity problem: encArg(0) -> 0 encArg(s(x_1)) -> s(encArg(x_1)) encArg(true) -> true encArg(false) -> false encArg(nil) -> nil encArg(add(x_1, x_2)) -> add(encArg(x_1), encArg(x_2)) encArg(cons_minus(x_1, x_2)) -> minus(encArg(x_1), encArg(x_2)) encArg(cons_quot(x_1, x_2)) -> quot(encArg(x_1), encArg(x_2)) encArg(cons_le(x_1, x_2)) -> le(encArg(x_1), encArg(x_2)) encArg(cons_app(x_1, x_2)) -> app(encArg(x_1), encArg(x_2)) encArg(cons_low(x_1, x_2)) -> low(encArg(x_1), encArg(x_2)) encArg(cons_if_low(x_1, x_2, x_3)) -> if_low(encArg(x_1), encArg(x_2), encArg(x_3)) encArg(cons_high(x_1, x_2)) -> high(encArg(x_1), encArg(x_2)) encArg(cons_if_high(x_1, x_2, x_3)) -> if_high(encArg(x_1), encArg(x_2), encArg(x_3)) encArg(cons_quicksort(x_1)) -> quicksort(encArg(x_1)) encode_minus(x_1, x_2) -> minus(encArg(x_1), encArg(x_2)) encode_0 -> 0 encode_s(x_1) -> s(encArg(x_1)) encode_quot(x_1, x_2) -> quot(encArg(x_1), encArg(x_2)) encode_le(x_1, x_2) -> le(encArg(x_1), encArg(x_2)) encode_true -> true encode_false -> false encode_app(x_1, x_2) -> app(encArg(x_1), encArg(x_2)) encode_nil -> nil encode_add(x_1, x_2) -> add(encArg(x_1), encArg(x_2)) encode_low(x_1, x_2) -> low(encArg(x_1), encArg(x_2)) encode_if_low(x_1, x_2, x_3) -> if_low(encArg(x_1), encArg(x_2), encArg(x_3)) encode_high(x_1, x_2) -> high(encArg(x_1), encArg(x_2)) encode_if_high(x_1, x_2, x_3) -> if_high(encArg(x_1), encArg(x_2), encArg(x_3)) encode_quicksort(x_1) -> quicksort(encArg(x_1)) ---------------------------------------- (2) Obligation: The Runtime Complexity (innermost) of the given CpxRelTRS could be proven to be BOUNDS(n^1, INF). The TRS R consists of the following rules: minus(x, 0) -> x popout

output may be truncated. 'popout' for the full output.

job log

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actions

all output return to Derivational Complexity: TRS Innermost